Understanding Rational Functions

The video tutorial explains the rational function f(x) = 4/x, focusing on determining its domain, creating a table of values, and graphing the function. It highlights the importance of avoiding division by zero, leading to a domain of all real numbers except x = 0. The video also discusses vertical and horizontal asymptotes, providing a step-by-step guide to plotting the function's graph. The tutorial concludes with a brief overview of the function's behavior as x approaches infinity.

What is the domain of the function f(x) = 4/x?

• All positive numbers

• All real numbers

• All real numbers except x = 0

• All negative numbers

Why is x = 0 excluded from the domain of f(x) = 4/x?

• Because it makes the function positive

• Because it makes the denominator zero

• Because it makes the numerator zero

• Because it makes the function negative

What is a vertical asymptote in the context of rational functions?

• A point where the graph intersects the x-axis

• A diagonal line the graph crosses

• A horizontal line the graph approaches

• A vertical line the graph approaches but does not cross

When creating a table of values for f(x) = 4/x, why is it helpful to choose values close to zero?

• To ensure all values are positive

• To make calculations easier

• To better understand the behavior near the asymptote

• To avoid negative values

Which x-values are convenient to choose for f(x) = 4/x?

• Values that are even numbers

• Values that are prime numbers

• Values that divide evenly into four

• Values that are multiples of ten

What is the value of f(x) when x = 2 for the function f(x) = 4/x?

• 4

• 8

• 2

• 1

What happens to the value of f(x) = 4/x as x approaches positive infinity?

• It approaches 4

• It approaches 0

• It approaches infinity

• It approaches -4

What is the horizontal asymptote of the function f(x) = 4/x?

• y = 4

• y = 0

• x = 4

• x = 0

How does the graph of f(x) = 4/x behave as x approaches negative infinity?

• It approaches -4

• It approaches 0

• It approaches infinity

• It approaches 4

What is the significance of a horizontal asymptote in a rational function?

• It is the point where the function is undefined

• It indicates where the graph crosses the x-axis

• It marks the maximum value of the function

• It shows the value the function approaches as x goes to infinity